Affine cellularity of affine $q$-Schur algebras

Weideng Cui

Published 2014-05-26, updated 2015-08-20Version 4

We first present an axiomatic approach to proving that an algebra with a cell theory in Lusztig's sense is affine cellular in the sense of Koenig and Xi, then we will show that the affine $q$-Schur algebra $\mathfrak{U}_{r,n,n}$ is affine cellular. We also show that $\mathfrak{U}_{r,n,n}$ is of finite global dimension and its derived module category admits a stratification when the parameter $v\in \mathbb{C}^{*}$ is not a root of unity.